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Counting on Letters

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Weekly Problem 31 - 2007

Stage: 3 Challenge Level: Challenge Level:1

Why do this problem?

This problem offers a good opportunity for students to work systematically.

Possible approach

This is a good starter question to have on the board as students enter the room.

Key questions

  • What numbers might go next to the 12?
  • How many ways of putting the numbers on the clock might there be?

Possible extension

  • Can the numbers 1 - 13 be arranged in a circle so that the pairs add up to a triangle number?

Possible support


This problem is taken from the UKMT Mathematical Challenges.

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